Question

What is the quotient?

Answer 1

Answer:

Option 3) $\frac{1}{(t+4)^{2}}$

Step-by-step explanation:

In the given question we have to calculate the quotient after division.

To solve this question we will factorize (t²+7t+12) first and then we will will divide by this.

⇒ t²+7t+12 = ( t²+4t+3t+12)

⇒ t(t+4)+3(t+4)

⇒ (t+3)(t+4)

Now its a simpler form of divisor to get the answer.

We come back to the question

$\frac{(t+3)}{t+4}\div(t^{2}+7t+12)$

$= \frac{(t+3)}{t+4}\div(t+3)(t+4)$

Or $=\frac{(t+3)}{t+4}\times\frac{1}{(t+3)(t+4)}$

$=\frac{1}{(t+4)^{2}}$

So the right answer is $\frac{1}{(t+4)^{2}}$